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# Probability, Confidence Interval & Hypothesis Testing

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See attached file for 3 problems: Tesla Motors, PC manufacturer and large insurance company claims

4. Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla's requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.

Descriptive statistics

count 16
mean 99.938
sample variance 2.313
sample standard deviation 1.521
minimum 97
maximum 102.9
range 5.9

population variance 2.169
population standard deviation 1.473

standard error of the mean 0.380

tolerance interval 95.45% lower 96.896
tolerance interval 95.45% upper 102.979
half-width 3.042

1st quartile 98.900
median 99.850
3rd quartile 100.475
interquartile range 1.575
mode 98.900

5. A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacture's claim, and explain your answer..

MegaStat Output
Hypothesis test for proportion vs. hypothesized value

Observed Hypothesized
0.085 0.05 p (as decimal)
9/100 5/100 p (as fraction)
8.5 5.0 X
100 100 n

0.0218 std. error
1.61 Z
.0541 p-value (one-tailed, upper)

6. The following table gives the number of claims at a large insurance company by kind and geographical region.
East South
Midwest
West
Totals

Hospitalization
102
98
39
62
301

Physician's Visit
263
514
120
351
1248

Outpatient Treatment
100
226
65
99
490

Totals
465
838
224
512
2039

(A) Referring to the above table, if a bill is chosen at random, what is the probability that it is either from the East or from the West?
(B) Referring to the above table, given that the bill is from the Midwest, what is the probability that it is for a Physician's Visit?

https://brainmass.com/statistics/hypothesis-testing/probability-confidence-interval-hypothesis-testing-337673

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval, hypothesis testing and probability. Formula for the calculation and Interpretations of the results are also included.

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## Statistics: probability, confidence interval, mean, standard deviation, test statistic

See attached four problems.

1. Avery short quiz has one multiple choice questions with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer any way.

a. What is the probability that you have given the correct answer to both questions?
b. What is the probability that only one of the two answers is correct?
c. What is the probability that neither answer is correct?
d. What is the probability that only your answer to the multiple choice question is correct?
e. What is the probability that you have only answered the true or false question correctly?

2. Information regarding the price of a roll of camera film (35 mm, 24 exposure) for a sample of 12 cities world wide is shown below. Determine 91% confidence interval for the population mean.

Price of film information is given in the attachment.

3. Confirmed cases of West Nile virus in birds for a sample of six countries in the state of Georgia are shown below.

Country Cases

Catoosa 6
Chattoogan 3
Gordon 5
Murray 3
Walker 4

You want to determine if the average number of cases of West Nile virus in the state of Georgia is significantly more than 3. Assume the population is normally distributed.

a. State the null and alternative hypotheses
b. Compute the mean and the standard deviation of the sample.
c. Compute the standard error of the mean.
d. Determine the test statistic.
e. Determine the P-value and 95% confidence, test the hypotheses.

4. Consider the following hypotheses test.

H0: mu >= 80
Ha: mu < 80

A sample of 121 provided a sample mean of 77.3. The population statndard deviation is known to be 16.5.

a. Compute the value of the test statistic.
b. Determine the P-value; and at 93.7% confidence, test the above hypotheses.
c. Using the critical value approach at 93.7% confidence, test the hypotheses.

5. In the last Presidential election, a national survey company claimed that no more than 50% (i.e., <=50%) of all registered voters voted for the Republican candidate. In a random sample of 400 registered voters, 208 voted for the Republican candidate.

a. State the null and alternative hypotheses
b. Compute the test statistic.
c. At 95% confidence, compute the P-value and test the hypotheses.

6. Consider the following hypothesis test:

H0: mu <= 38
Ha: mu > 38

You are given the following information obtained from a random sample of six observations. Assume the population has a normal distribution.

X
38
40
42
32
46
42
a. Compute the mean of the sample.
b. Determine the standard deviation of the sample.
c. Determine the standard error of the mean.
d. Compute the value of the test statistic.
e. At 95% confidence using the P-value approach, test the above hypotheses.

7. A test on world history was given to a group of individuals before and also after a film on the history of the world was presented. The results are given in the attachment. We want to determine if the film significantly increased the test scores.

a. Give the hypotheses for this problem.
b. Compute the test statistic.
c. At 95% confidence, test the hypotheses.

8. The Dean of students at UTC has said that the average grade of UTC students is higher than that of the students at GSU. Random samples of grades from the two schools are selected, and the results are shown in the attachment.

a. Give the hypotheses.
b. Compute the degrees of freedom for this test.
c. Compute the test statistic.
d. At a 0.1 level of significance, test the Dean of Student's statement.

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